Suppose and are differentiable on with and for all

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Suppose

f

and

g

are differentiable on

\mathbb R

with

f(0)=g(0)

and

(f-g)'(x)>0

for all

x\ne0

. How many real solutions can the equation

f(x)=g(x)

have? Justify briefly.